Heat Release Rate (HRR)
Calculate the heat release rate of a fire (HRR), Q̇ = ṁ × ΔH_c, multiplying the fuel burning rate (kg/s) by the effective heat of combustion (MJ/kg). The result, in MW, is the fire's power — the single most important quantity in fire science, governing gas temperatures, flame height, smoke production and spread rate. It is the fundamental input to fire safety engineering models and to the design of smoke control and detection systems. Enter the burning rate and the heat of combustion.
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Heat release rate (HRR)
If a single quantity defines a fire, it is the heat release rate (HRR, also written rate of heat release) — the power of the fire. It is the product of the fuel burning rate ṁ (mass consumed per second, kg/s) and the effective heat of combustion ΔH_c (energy released per kg, MJ/kg): Q̇ = ṁ × ΔH_c, in MW. The HRR governs practically everything in the development of a fire: the gas temperature in the hot layer, the flame height, the flow of the smoke plume, the radiation emitted (and hence the spread to other objects), the onset of flashover (the sudden generalised ignition of a compartment) and the growth speed of the fire. That makes the HRR the central input of all performance-based fire safety engineering: from it, zone and field (CFD) models compute temperatures, visibility and tenability, size smoke control systems, place detectors and check whether the available escape time exceeds the required one. Real fires get described by an HRR-versus-time curve, frequently the 't²' model, in which power grows with the square of time. A wastebasket releases ~5 kW; a sofa, 1–3 MW; a car, ~5 MW. Enter the burning rate and the heat of combustion.
Related Tools
Smoke Plume Mass Flow
Calculate the mass flow of a fire's smoke plume by the Heskestad correlation, ṁ = 0.071·Q̇_c^(1/3)·z^(5/3), from the convective part of the heat release rate Q̇_c (kW) and the height above the fire base z (m). The result, in kg/s, is the amount of hot gases and smoke rising and accumulating, governing the design of smoke control and exhaust systems (mechanical or natural) that keep a smoke-free layer for safe evacuation. The flow grows strongly with height. Enter the convective heat fraction and the height.
Bearing Power Loss
Calculate the power dissipated by friction in a bearing, P = T × ω, multiplying the friction torque T by the angular velocity ω (rad/s). The result, in watts, is the mechanical energy converted to heat per unit time by friction — a loss that reduces efficiency and heats the lubricant and components. This heat must be dissipated (by convection or oil circulation) to keep a safe operating temperature, since overheating degrades the lubricant and can cause seizure. Estimating the dissipated power is essential to size the cooling and the oil flow. Enter the friction torque and the angular velocity.
Stack Heat Loss (Siegert)
Calculate the heat loss through the exhaust gases by the Siegert formula, loss = K × (T_gas − T_air) ÷ CO₂, from the fuel factor K (~0.5 for natural gas, ~0.6 for oil), the gas and combustion air temperatures (°C) and the CO₂ percentage in the gases. The result, in %, is the largest energy loss of a boiler or furnace — the heat escaping hot through the stack. Lowering the gas temperature (with economizers and preheaters) and adjusting the excess air (which dilutes CO₂) minimizes this loss. The combustion efficiency is approximately 100% minus this loss. Enter the K factor, the temperatures and the CO₂.
Flame Height (Heskestad)
Estimate the mean height of a diffusion flame by the Heskestad correlation, L = 0.235·Q̇^(2/5) − 1.02·D, from the heat release rate Q̇ (kW) and the fire base diameter D (m). The result, in metres, is the visible flame height above the base — essential to assess the risk of fire spread by radiation, the thermal reach over structures and the activation of detectors and sprinklers. Height grows with the fire power to the 2/5 power and decreases with the base diameter. It is one of the classic fire dynamics correlations. Enter the heat release rate and the base diameter.
Brake Power Dissipated
Calculate the power dissipated by a brake under torque, P = T·(2π·n/60), from the braking torque T (N·m) and the rotation n (rpm). Dissipated power is the rate at which the brake converts mechanical energy to heat — the product of braking torque and angular velocity. It differs from total braking ENERGY: energy is the total heat generated (joules), while power is the INTENSITY of that heat generation (watts), and it determines the brake's steady-state temperature. A brake dissipating much energy but slowly (low power) heats little; one dissipating the same energy fast (high power) heats much more. Dissipated power is critical in brakes working CONTINUOUSLY or repetitively: retention brakes on long descents, industrial equipment brakes (hoists, cranes, conveyors holding load), and dynamometers (which measure engine power precisely by dissipating it in a brake). There, the steady-state dissipated power sets the COOLING capacity needed (ventilation, water cooling) to keep temperature stable. Equating dissipated power to cooling capacity gives the equilibrium temperature. Enter the braking torque and the rotation.
eGFR (MDRD)
Estimates GFR via simplified MDRD using serum creatinine, age, sex and ethnicity.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.